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Lecture Notes for STAT 2004 - Introductory Statistics at Virginia Tech (VT)

Notes Information

Material Type:CribSheet
Professor:Staff
Class:STAT 2004 - Introductory Statistics
Subject:Statistics
University:Virginia Polytechnic Institute And State University
Term:Spring 2006
Keywords:
  • No Correlation
  • Achievement
  • Sample Correlation
  • Strong Correlation
  • Relationship
  • Observation
  • Linear Relationship
  • Interpretation
  • Positive Correlation
  • Correlation Coefficient (r)
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10.1 THE LINEAR CORRELATION COEFFICIENT • Sample correlation coefficient, r, is measure of degree of linear relationship between two variables in the sample • Formula : r= Sxy/SxSy where Sxy= [(X-X)(Y-Y)]/n-1 * Different from formula in book (ignore formulas in book) 10.2 EXAMPLE: "BEHAVIOR AND ACHIEVEMENT" As part of a study on grade school children, a researcher wanted to investigate the relationship between behavior in school (X) and an index of academic achievement (Y). Compute the sample correlation coefficient using the following data for five randomly selected children. Behavior (X) Achievement (Y) 7 15 1 7 14 12 3 5 5 11 X Y (X-X) (X-X)^2 (Y-Y) (Y-Y)^2 (X-X) (Y-Y) 7 15 1 1 5 25 5 17 –5 25 –3 9 15 14 12 8 64 2 4 16 35 –3 9 –5 25 15 5 11 –1 1 1 1 –1 30 50 0 100 0 64 50 Values of r • Range: –1 ≤ r ≤ +1 • Positive correlation (r > 0) * High values on X tend to go with high values on Y, Low values on X with low values on Y * Plot (X,Y) points: best-fitting line slopes up to right ...

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